Approximation of analytic functions by Bessel functions of fractional order

• Date: 2011
• Main Authors: Jung, S.-M., Юнг, С. М.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2835
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We solve the inhomogeneous Bessel differential equation $$x^2y''(x) + xy'(x) + (x^2 - \nu^2)y(x) = \sum^{\infty}_{m=0} a_mx^m$$, where $\nu$ is a positive nonintegral number, and use this result for the approximation of analytic functions of a special type by the Bessel fu...